Timeline for Max-root inequality for convex combination of real-stable monic polynomials (Kadison-Singer Problem)
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 24, 2021 at 13:59 | comment | added | Iosif Pinelis | @Strickland : (i) Such multiple roots cannot exist, because $R(u)u^{l-k}$ has a nonzero derivative in those right and left neighborhoods. I have now added this additional explanation. (ii) I have also added details on $m(p)<m(q)$. | |
| Mar 24, 2021 at 13:56 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 282 characters in body
|
| Mar 24, 2021 at 6:41 | comment | added | Strickland | Thanks for the clarification. If still have some questions though, if you do not mind. 1. When you argue that $R(u)u^{l-k}+s=0$ has no more than two roots $u$ resp. one, I assume you base this on monotonicity. However, could it not have a root of multiplicity 4 for example? 2. It is immediately assumed that $m(p)<m(q)$. What if they are equal? | |
| Mar 24, 2021 at 6:35 | vote | accept | Strickland | ||
| Mar 23, 2021 at 16:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 3 characters in body
|
| Mar 23, 2021 at 14:20 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
edited body
|
| Mar 23, 2021 at 14:11 | comment | added | Iosif Pinelis | @Strickland : Thank you for your comment. Somehow, I thought only of the roots of $q$ in $(0,1)$ of odd multiplicities. This is now fixed. | |
| Mar 23, 2021 at 14:05 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 279 characters in body
|
| Mar 23, 2021 at 13:58 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 279 characters in body
|
| Mar 23, 2021 at 6:41 | comment | added | Strickland | Thanks a lot. If I understand correctly, the argument for case 1 seems a continuity argument of sort $\lim_{t_n\to t_*} m(q_{t_n})=m(q_{t_*})>m_p=0$, which leads to the contradiction. Did I understand this correctly? If so, is it clear that $m()$ is continuous and secondly, why wouldn't this hold for case 2 as well? | |
| Mar 22, 2021 at 22:02 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 3105 characters in body
|
| Mar 22, 2021 at 19:23 | history | undeleted | Iosif Pinelis | ||
| Mar 22, 2021 at 17:50 | history | deleted | Iosif Pinelis | via Vote | |
| Mar 22, 2021 at 17:39 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |